MEMOIR OF LEGENDRE. 147 



sary complement of the metrical system, required new trigonometrical tables. 

 M. de Prony caused them to be constructed, with incredible celerity, by means 

 of the division of labor and by processes wholly new, which admitted of the 

 emploj'raent of arithmeticians of even the most indifferent qualifications. The 

 work was prepared by a section of analysts, over which presided M. Legendre, 

 who contributed greatly to facilitate the operation by devising new and ingen- 

 ious formulas for determining the successive differences of the sinus. For the 

 other sections it only remained to make the additions. The labors of this 

 board of calculation [)roduced two copies of tables entirely independent one of 

 the other, and affording, by their identity, a mutual verilication. This monu- 

 ment of labor and skill, the most vast of its kind which has ever been executed 

 or even conceived, has no other defect, said JM. Delambre, but its verij immen- 

 sity, which has so long delayed its publication. 



When the revolutionary tempest had begun to subside, one of the first cares 

 of government was to reorganize public instruction ; but M. Legendre, whether 

 he was not in favor with the men in power or for whatever other reason, was not 

 invited to co-operate. His name does not either figure at the close of 1794 

 among those of the first professors of the Polytechnic school, nor in January, 

 1795, in the list of the professors of the Normal schools ; nor yet Avas he com- 

 prised among the 48 savants whom the government selected to form the nucleus 

 of the Institute ; but, at the earliest opportunity, his colleagues hastened to 

 redress this injustice by summoning him to their ranks. It will not be amiss to 

 recall here the succession of events, as facts not destitute of historical interest. 



The Academ^^ of Sciences having been suppressed by a decree of the conven- 

 tion of the 8th of xiugust, 1793, the National Institute, of which the first class 

 represented that academ}', was established by a law of the 5 fructidor, year III, 

 (22d August, 1795,) and was organized by a second law of the 3 brinii aire, year 

 IV, (25th October, 1795.) By the ninth article of this law it was enacted that, 

 " for the formation of the National Institute, the Executive Directory shall 

 nominate 48 members, who shall elect 96 others." To form the nucleus of the 

 first class of the Institute, 20 members were accordingly nominated by the 

 director}', December G, 1795, being two for each section ; those for the section 

 of mathematics were j\OI. Lagrange and Laplace. Two other members, MM. 

 ]3orda and Bossut, were elected in the meeting of the 9th of December, and the 

 section, which was to ha composed of six members, Avas completed on the 13th 

 of the same month by the election of MM. Legendre and Delambre. In this 

 list M. Bossut appeared by just title for his labors in hydraulics; MM. Borda 

 and Delambre Avere included Avith not less right for their important services in 

 relation to geodesy, to measiu"es of precision and astronomical calculations ; 

 MM. Lagrange, Laplace and Legendre Avere essentially the representatives of 

 Lhe higher analysis, and occupied during life the foremost place among the geom- 

 eters of the Institute. All three continued till death to justify this proud posi- 

 tion by labors Avorthy of themselves and of the illustrious body to which it Avas 

 their pleasure as Avell as duty to communicate them. 



In 1805 M. Legendre published new methods for the determination of the 

 orbits of comets, to Avhich he added, in 1806 and 1820, two supplements j in 

 the latter stages of life he liad collected the most recent observations on comets 

 of short periods, in the design of still further applying and improAnng his pro- 

 cesses of calculation. Previous to the publication of his two first memoir;^ in 

 1805 and 1806, the question had, in his opinion, been alwaj'S treated in an 

 imperfect manner and merely by approximations. He considered himself as 

 having first indicated two certain modes of arriving at a solution, at once the 

 most simple and exact, namely, ihc method of indeterminate corrections, pro- 

 posed by him as earlv as 1787, but the applications of Avhich had been few in 

 number, and the method of least squares, which then appeared for the first time. 

 Nevertheless, this analytic perfection, to Avhich the author sought to add as often 

 as he retouched his formulas, has seemed to astronomers to be more than coun- 



